A Eurosceptic business group supported by executives including the former Marks & Spencer boss Sir Stuart Rose and the Next chief executive Lord Wolfson will argue on Tuesday that the vast majority of British companies should be exempt from EU regulations.

Amid deepening Tory divisions over Europe, the Business for Britain group is calling for 95% of all British firms to be freed from EU regulations on the grounds that they conduct no trade with other EU countries. The organisation says that only British businesses that trade with the EU – 5% of the total – should be subject to single-market regulations.

The report is published as Conservative Eurosceptics who are pressing David Cameron to give parliament a veto over all EU laws ran into trouble when it emerged that they mistakenly claimed to have the support of one of the most senior backbench Tory MPs.

Andrew Tyrie, the chairman of the commons treasury select committee, told the BBC that he was wrongly listed as a signatory of a letter to the prime minister and he knew of six other Tory MPs who were also wrongly listed. Tyrie said he had seen the letter but did not agree with all of it.

The remarks by Tyrie came as a blow to Bernard Jenkin, the arch Eurosceptic Tory chairman of the commons public administration select committee, who claimed to have the signatures of at least 95 fellow MPs for his letter to the prime minister calling for parliament to be given a veto over EU laws. Jenkin, who faced a major operation by the Tory whips to undermine his letter, told the BBC: "We cannot trace how his name got on to the list but we are, as we speak, adding other names."

The Eurosceptic group Business for Britain calls for a "British option" to exempt all but a handful of UK companies from "burdensome EU regulations".

But the pro-European British Influence group described the proposal as "laughable", because the report makes little distinction between a corner shop and a car manufacturer such as Nissan. The report does admit that the value of UK exports to the EU account for 14% of the UK's GDP – equivalent to nearly £200bn a year.

A YouGov survey of 1,024 business leaders commissioned for the report found that 46% said costs of EU regulations, estimated at about £7.5bn a year, outweigh the benefits. Just over a third (37%) took the opposite view.

Matthew Elliott, the group's chief executive who co-authored the report, said: "Many different, often complex ideas have been advanced to improve or refine the single market in the EU, but none have yet tackled the huge regulatory and financial burden it places on the 95% of companies that don't even export to the continent. By excluding these firms and organisations that don't need access to the single market from the most burdensome aspects of EU regulation, the government would, at a stroke, better position Britain in the UK global race.

"It is clear from our survey of the business community that they want a forward- looking relationship with the EU based on trade rather than politics. Business leaders want access to the single market for the 5% of firms that trade with the EU, but they also want to make Britain more competitive in the global race and to ensure that we are better able to trade with the high-growth areas of the world."

Martin Barker, managing director of engineers Rowan Precision, who supports the Our Biggest Market campaign run by British Influence, said: "This is a laughable plan. You can't have a two-tier system. What will happen to companies who are looking to export?"

Jonathan Williams, chief executive of Marine South East, who is also a supporter of British Influence, added: "This proposal can only be described as utterly naive. European customers and suppliers are integral to the UK's business base."

Vince Cable, the business secretary, said: "One in 10 jobs in the UK rely on trade with the EU. By being in the EU, British businesses also benefit from a common set of rules to do business and attract foreign investors. We should be supporting all British businesses to take advantage of the single market, not holding them back by shutting the door on the biggest trading block in the world."

Roland Rudd, chairman of the pro-European Business for New Europe, said: "If Business for Britain's plans were implemented, they would threaten British exports and divert attention from reforming the EU, to make it better for all 28 members."

Europe has flared up again as eurosceptics put pressure on the prime minister ahead of his attempted renegotiation of Britain's EU membership terms, which cannot begin formally until he wins an overall parliamentary majority or he secures agreement with the Liberal Democrats in a fresh coalition agreement.

Government sources acknowledge that having 16 months until the election has created a vacuum that is being filled by campaigners on both sides.

Mainstream Eurosceptics will have their chance on Wednesday and Thursday this week when the pro-reform Open Europe thinktank hosts a conference with the Fresh Start group of Tory MPs.